Reduction of Kinetic Equations to Liénard-Levinson-Smith Form: Counting Limit Cycles

Abstract

We have presented an unified scheme to express a class of system of equations in two variables into a Liénard-Levinson-Smith (LLS) oscillator form. We have derived the condition for limit cycle with special reference to Rayleigh and Liénard systems for arbitrary polynomial functions of damping and restoring force. Krylov-Boguliubov (K-B) method is implemented to determine the maximum number of limit cycles admissible for a LLS oscillator atleast in the weak damping limit. Scheme is illustrated by a number of model systems with single cycle as well as the multiple cycle cases.

arXiv comment9 Pages, Published online on 29/03/2019

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Cited by in corpus (3)

• Systematic designing of bi-rhythmic and tri-rhythmic models in families of Van der Pol and Rayleigh oscillators
• Where the Liénard--Levinson--Smith (LLS) theorem cannot be applied for a generalised Liénard system
• Microscopic quantum generalization of classical Liénard oscillators